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Simplifying 0.3(3z + 6) + 43.4 = 0.7(3z + -4) Reorder the terms: 0.3(6 + 3z) + 43.4 = 0.7(3z + -4) (6 * 0.3 + 3z * 0.3) + 43.4 = 0.7(3z + -4) (1.8 + 0.9z) + 43.4 = 0.7(3z + -4) Reorder the terms: 1.8 + 43.4 + 0.9z = 0.7(3z + -4) Combine like terms: 1.8 + 43.4 = 45.2 45.2 + 0.9z = 0.7(3z + -4) Reorder the terms: 45.2 + 0.9z = 0.7(-4 + 3z) 45.2 + 0.9z = (-4 * 0.7 + 3z * 0.7) 45.2 + 0.9z = (-2.8 + 2.1z) Solving 45.2 + 0.9z = -2.8 + 2.1z Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-2.1z' to each side of the equation. 45.2 + 0.9z + -2.1z = -2.8 + 2.1z + -2.1z Combine like terms: 0.9z + -2.1z = -1.2z 45.2 + -1.2z = -2.8 + 2.1z + -2.1z Combine like terms: 2.1z + -2.1z = 0.0 45.2 + -1.2z = -2.8 + 0.0 45.2 + -1.2z = -2.8 Add '-45.2' to each side of the equation. 45.2 + -45.2 + -1.2z = -2.8 + -45.2 Combine like terms: 45.2 + -45.2 = 0.0 0.0 + -1.2z = -2.8 + -45.2 -1.2z = -2.8 + -45.2 Combine like terms: -2.8 + -45.2 = -48 -1.2z = -48 Divide each side by '-1.2'. z = 40 Simplifying z = 40
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